She consulted Phones4u, a bulk discounter of cellphones and data packages, which offered her a free iPhone 4S and data plan for £2, or $3.20, more than what she had been paying each month. She returned to her operator, O2 U.K., which had been selling the 4S for £99 with the same plan. She told people there about the rival offer.

“They didn’t blink an eye,” Ms. Turner said. “They matched it.”

Apple , the global market leader in smartphones, is enjoying record profits and sales that have transformed it into one of the world’s most valuable companies. But the mobile computing industry it has conquered in just five years is changing rapidly, and nothing, not even Apple’s vaunted brand premium — the ability to charge more than its competitors for premium smartphones — appears guaranteed.